Thursday, July 05, 2007

Mutation Rates

Each of us was born with at least 350 new mutations that make our DNA different from that of our parents.

Douglas Futuyma (2005) p. 162Let’s think about the number of mutations that could accumulate in a population over time. A few pages ago we looked at the origin of antibiotic resistance in bacteria in order to prove that mutations occur randomly. Now we’ll consider just how frequency those mutations could arise in bacteria. Then we’ll ask how frequently mutations occur in humans.

Our model bacterium is Esherichia coli the common, and mostly benign, intestinal bacterium. The entire genome was sequenced in 1997 (Blattner et al., 1997) and its size is 4,200,000 base pairs (4.2 × 106 bp). Every time a bacterium divides this amount of DNA has to be replicated; that’s 8,400,000 nucleotides (8.4 × 106).

The most common source of mutation is due to mistakes made during DNA replication when an incorrect nucleotide is incorporated into newly synthesized DNA. The mutation rate due to errors made by the DNA polymerase III replisome is one error for every one hundred million bases (nucleotides) that are incorporated into DNA. This is an error rate of 1/100,000,000, commonly written as 10-8 in exponential notation. Technically, these aren't mutations; they count as DNA damage until the problem with mismatched bases in the double-stranded DNA has been resolved. The DNA repair mechanism fixes 99% of this damage but 1% escapes repair and becomes a mutation. The error rate of repair is 10-2 so the overall error rate during DNA replication is 10-10 nucleotides per replication (10-8 × 10-2) (Tago et al., 2005).

Since the overall mutation rate is lower than the size of the E. coli genome, on average there won’t be any mistakes made when the cell divides into two daughter cells. That is, the DNA will usually be replicated error free.

However, one error will occur for every 10 billion nucleotides (10-10) that are incorporated into DNA. This means one mutation, on average, every 1200 replications (8.4 × 106 × 1200 is about ten billion). This may not seem like much even if the average generation time of E. coli is 24 hours. It would seem to take four months for each mutation. But bacteria divide exponentially so the actual rate of mutation in a growing culture is much faster. Each cell produces two daughter cells so that after two generations there are four cells and after three generations there are eight cells. It takes only eleven generations to get 2048 cells (211 = 2048). At that point you have 2048 cells dividing and the amount of DNA that is replication in the entire population is enough to ensure at least one error every generation.

In the laboratory experiment the bacteria divided every half hour so after only a few hours the culture was accumulating mutations every time the bacteria divided. This is an unrealistic rate of growth in the real world but even if bacteria only divide every 24 hours there are still so many of them that mutations are abundant. For example, in your intestine there are billions and billions of bacteria. This means that every day these bacteria accumulate millions of mutations. That’s why there’s a great danger of developing drug resistance in a very short time.

Calculating the rate of evolution in terms of nucleotide substitutions seems to give a value so high that many of the mutations must be neutral ones.

Motoo Kimura (1968)I based my estimate of mutation rate on what we know about the properties of the replisome and repair enzymes. Independent measures of mutation rates in bacteria are consistent with this estimate. For example, the measured value for E. coli is 5.4 × 10-10 per nucleotide per replication (Drake et al., 1998). Many of these mutations are expected to be neutral. The rate of fixation of neutral mutations is equal to the mutation rate so by measuring the accumulation of neutral mutations in various lineages of bacteria you can estimate the mutation rate provided you know the time of divergence and the generation time. (Ochman et al., 1999) have estimated that the mutation rate in bacteria is close to 10-10 assuming that bacteria divide infrequently.

The mutation rate in eukaryotes should be about the same since the properties of the DNA replication machinery are similar to those in eukaryotes. Measured values of mutation rates in yeast, Caenorhabditis elegans, Drosophila melanogaster, mouse and humans are all close to 10-10 (Drake et al., 1998).

The haploid human genome is about 3 × 109 base pairs in size. Every time this genome is replicated about 0.3 mutations, on average, will be passed on to one of the daughter cells. We are interested in knowing how many mutations are passed on to the fertilized egg (zygote) from its parents. In order to calculate this number we need to know how many DNA replications there are between the time that one parental zygote was formed and the time that the egg or sperm cell that unite to form the progeny zygote are produced.

In the case of females, this number is about 30, which means that each female egg is the product of 30 cell divisions from the time the zygote was formed (Vogel and Rathenberg, 1975). Human females have about 500 eggs. In males, the number of cell divisions leading to mature sperm in a 30 year old male is about 400 (Vogel and Motulsky, 1997). This means that about 9 mutations (0.3 × 30) accumulate in the egg and about 120 mutations (0.3 × 400) accumulate in a sperm cell. Thus, each newly formed human zygote has approximately 129 new spontaneous mutations. This value is somewhat less than the number in most textbooks where it's common to see 300-350 mutations per genome. The updated value reflects a better estimate of the overall rate of mutation during DNA replication and a better estimate of the number of cell divisions during gametogenesis.

With a population of 6 billion individuals on the planet, there will be 120 × 6 × 109 = 7.2 × 1011 new mutations in the population every generation. This means that every single nucleotide in our genome will be mutated in the human population every 20 years or so.

11 comments
:

These calculations seem reasonable for the mutation rate in zygotes, but isn't there another step between estimating the rate in the general population? I'm sure plenty of those mutations can end in premature death of the embryo, thus effectively eliminating some mutations from the population. Furthermore, mutations may not be Poisson distributed but could instead clump, giving rise to a small set of highly mutated and a large set of sparsely mutated gametes.

Well done, but you might want to revise up the base mutation rate by about an order of magnitude, based on the results of this direct sequencing study, especially since you're explicitly considering neutral rates:

DGS, there are many studies that confirm a base mutation rate of 10^-10 nucleotides per replication. You don't throw those out every time a new paper is published with a value that contradicts the established values.

One of the most difficult things to understand about science is how to discriminate among papers that conflict. Most people seem to think that every single paper is given exactly the same weight in making a decision about the correct view of biology. That's why the popular version of science imagines that scientists are in a constant state of flux, changing their views from one day to the next as this week's issue of Nature arrives in the mail.

That's not how science works. I've looked at the paper you mentioned but for now I'll file it under "interesting but probably wrong." If that pile gets too big I'll think about revising my estimate of mutation rate but for now there are far more papers filed under "interesting and probably correct."

Very nice post that I intend to use with my students in the Fall.Would it be possible to extend these calculations to determine how much sequence divergence should be observed between human and chimpanzee based on their estimated last common ancestor? This estimation should come close to the observed value of 99% similarity right?

I have a question. An obvious "improvement" in improving the fidelity of stem cells would be to segregate the two daughter cells and preserve the one that had the "original" half strand. Has anyone looked to see if that happens or not?

There was a study on DNA in the brains of individuals exposed to higher C14 from atmospheric nuclear tests, and it showed the DNA of neurons had the C14 content characteristic of childhood exposure.

It might be very hard to see in vivo if the segregation is even slighyly imperfect.

Larry said... DGS, there are many studies that confirm a base mutation rate of 10^-10 nucleotides per replication. You don't throw those out every time a new paper is published with a value that contradicts the established values.

One of the most difficult things to understand about science is how to discriminate among papers that conflict. Most people seem to think that every single paper is given exactly the same weight in making a decision about the correct view of biology. That's why the popular version of science imagines that scientists are in a constant state of flux, changing their views from one day to the next as this week's issue of Nature arrives in the mail.

I'm not an idiot, Larry, and I don't think you are, either. This is not a flavor-of-the-week sort of issue. There is a fundamental difference in direct vs. indirect mutation rate estimates. There are plenty of good reasons to think that the direct mutation rate, the actual rate of appearance of mutations from one generation to the next, is going to be higher than the rate of fixed mutations, which is the rate that shows up in phylogenetically-oriented studies, or other studies that are not explicitly designed to enhance the fixation of mutations generally and do not directly observe these mutations. And while the Denver et al. paper is certainly not the last word on the subject (Brian Charlesworth's lab provided a Drosophila-oriented estimate using HPLC that is not so high) it does provide pretty good support for higher rates of direct mutation.

I like what you did. It's just that, in my view, you're talking about an apple, and I'm talking about a bigger apple, which is much harder to measure, so most people ignore it. But I think it's at least reasonable to think of the bigger apple as the true "opportunity" created by mutation, hence the relevance of my comment within the context of your post.

I'm not an idiot, Larry, and I don't think you are, either. This is not a flavor-of-the-week sort of issue. There is a fundamental difference in direct vs. indirect mutation rate estimates. There are plenty of good reasons to think that the direct mutation rate, the actual rate of appearance of mutations from one generation to the next, is going to be higher than the rate of fixed mutations, which is the rate that shows up in phylogenetically-oriented studies, or other studies that are not explicitly designed to enhance the fixation of mutations generally and do not directly observe these mutations. And while the Denver et al. paper is certainly not the last word on the subject (Brian Charlesworth's lab provided a Drosophila-oriented estimate using HPLC that is not so high) it does provide pretty good support for higher rates of direct mutation.

A mutation rate of 10^-10 is consistent with the known in vitro error rates in DNA replication and repair. If you want to increase that error rate by a factor of ten then you should try and explain how the extra mutations are created.

Are you suggesting that most (9/10) mutations are generated by something other than errors in DNA replication or are you suggesting that DNA replication/repair is more error prone in vivo than it is in vitro?

Recall that I base my estimate on the biochemistry of the process and not measured mutation rates in populations. The fact that the population rates are (mostly) consistent is satisfying but because they are indirect they are less convincing to me than the direct measurements. (And, yes, I am aware of the difference between mutation rates and fixation rates.)

We know that there are regions of the genome that are error prone. The error rates in these regions can easily be ten or a hundred times higher.

In regards to the comments on the debated rate, at least in bacteria nobody has estimated the spontaneous mutation rate in a statistically satisfying way (at least to my knowledge, though would love to know otherwise!).

Basically, all of the good data comes from fluctuation assays, which only estimate a rate at which a phenotype appears (and these estimates are often downward biased because a lot use rif resistance as the phenotype, and don't account for how much slower resistant mutants grow in the analysis). Also, converting a phenotypic rate to a genomic mutation rate is very difficult. The spectrum of mutations that are available to confer resistance are not the same as those available to the entire genome, and so a lot of sequencing has to be done to determine what mutants were available, and then a comparison must be made to the entire genome. I know of no study that has done this so far, or estimated the uncertainty that carries through, I don't think we as a community have the rate down to right within an order of magnitude for prokaryotes, though much better work has been done in eukaryotes.

Laurence A. Moran

Larry Moran is a Professor Emeritus in the Department of Biochemistry at the University of Toronto. You can contact him by looking up his email address on the University of Toronto website.

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The old argument of design in nature, as given by Paley, which formerly seemed to me to be so conclusive, fails, now that the law of natural selection has been discovered. We can no longer argue that, for instance, the beautiful hinge of a bivalve shell must have been made by an intelligent being, like the hinge of a door by man. There seems to be no more design in the variability of organic beings and in the action of natural selection, than in the course which the wind blows.Charles Darwin (c1880)Although I am fully convinced of the truth of the views given in this volume, I by no means expect to convince experienced naturalists whose minds are stocked with a multitude of facts all viewed, during a long course of years, from a point of view directly opposite to mine. It is so easy to hide our ignorance under such expressions as "plan of creation," "unity of design," etc., and to think that we give an explanation when we only restate a fact. Any one whose disposition leads him to attach more weight to unexplained difficulties than to the explanation of a certain number of facts will certainly reject the theory.

Charles Darwin (1859)Science reveals where religion conceals. Where religion purports to explain, it actually resorts to tautology. To assert that "God did it" is no more than an admission of ignorance dressed deceitfully as an explanation...

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The world is not inhabited exclusively by fools, and when a subject arouses intense interest, as this one has, something other than semantics is usually at stake.
Stephen Jay Gould (1982)
I have championed contingency, and will continue to do so, because its large realm and legitimate claims have been so poorly attended by evolutionary scientists who cannot discern the beat of this different drummer while their brains and ears remain tuned to only the sounds of general theory.
Stephen Jay Gould (2002) p.1339
The essence of Darwinism lies in its claim that natural selection creates the fit. Variation is ubiquitous and random in direction. It supplies raw material only. Natural selection directs the course of evolutionary change.
Stephen Jay Gould (1977)
Rudyard Kipling asked how the leopard got its spots, the rhino its wrinkled skin. He called his answers "just-so stories." When evolutionists try to explain form and behavior, they also tell just-so stories—and the agent is natural selection. Virtuosity in invention replaces testability as the criterion for acceptance.
Stephen Jay Gould (1980)
Since 'change of gene frequencies in populations' is the 'official' definition of evolution, randomness has transgressed Darwin's border and asserted itself as an agent of evolutionary change.
Stephen Jay Gould (1983) p.335
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Stephen Jay Gould (1999) p.84

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My own view is that conclusions about the evolution of human behavior should be based on research at least as rigorous as that used in studying nonhuman animals. And if you read the animal behavior journals, you'll see that this requirement sets the bar pretty high, so that many assertions about evolutionary psychology sink without a trace.

Jerry Coyne
Why Evolution Is TrueI once made the remark that two things disappeared in 1990: one was communism, the other was biochemistry and that only one of them should be allowed to come back.

Sydney Brenner
TIBS Dec. 2000
It is naïve to think that if a species' environment changes the species must adapt or else become extinct.... Just as a changed environment need not set in motion selection for new adaptations, new adaptations may evolve in an unchanging environment if new mutations arise that are superior to any pre-existing variations

Douglas Futuyma
One of the most frightening things in the Western world, and in this country in particular, is the number of people who believe in things that are scientifically false. If someone tells me that the earth is less than 10,000 years old, in my opinion he should see a psychiatrist.

Francis Crick
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Sydney Brenner
An atheist before Darwin could have said, following Hume: 'I have no explanation for complex biological design. All I know is that God isn't a good explanation, so we must wait and hope that somebody comes up with a better one.' I can't help feeling that such a position, though logically sound, would have left one feeling pretty unsatisfied, and that although atheism might have been logically tenable before Darwin, Darwin made it possible to be an intellectually fulfilled atheist

Richard Dawkins
Another curious aspect of the theory of evolution is that everybody thinks he understand it. I mean philosophers, social scientists, and so on. While in fact very few people understand it, actually as it stands, even as it stood when Darwin expressed it, and even less as we now may be able to understand it in biology.

Jacques Monod
The false view of evolution as a process of global optimizing has been applied literally by engineers who, taken in by a mistaken metaphor, have attempted to find globally optimal solutions to design problems by writing programs that model evolution by natural selection.